DOA Estimation of High-Dimensional Signals Based on Krylov Subspace and Weighted $l_{1}$-Norm

Abstract

With the extensive application of large-scale array antennas, the increasing number of array elements leads to the increasing dimension of received signals, making it difficult to meet the real-time requirement of direction of arrival (DOA) estimation due to the computational complexity of algorithms. Traditional subspace algorithms require estimation of the covariance matrix, which has high computational complexity and is prone to producing spurious peaks. In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements, this paper proposes a DOA estimation method based on Krylov subspace and weighted $l_{1}$ -norm. The method uses the multistage Wiener filter (MSWF) iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace, further uses the measurement matrix to reduce the dimensionality of the signal subspace observation, constructs a weighted matrix, and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted $l_{1}$ -norm to solve the target DOA. Simulation results show that the proposed method has high resolution under large array conditions, effectively suppresses spurious peaks, reduces computational complexity, and has good robustness for low signal to noise ratio (SNR) environment.